Question: Solve for $x$ : $5x^2 - 10x - 40 = 0$
Dividing both sides by $5$ gives: $ x^2 {-2}x {-8} = 0 $ The coefficient on the $x$ term is $-2$ and the constant term is $-8$ , so we need to find two numbers that add up to $-2$ and multiply to $-8$ The two numbers $-4$ and $2$ satisfy both conditions: $ {-4} + {2} = {-2} $ $ {-4} \times {2} = {-8} $ $(x {-4}) (x + {2}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x + 2) = 0$ $x - 4 = 0$ or $x + 2 = 0$ Thus, $x = 4$ and $x = -2$ are the solutions.